This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...

Solutions to the optimal H , and L2 L, unbiased reduced-order filtering problems are obtained in terms of Linear Matrix Inequalities (LMIs). The order of the optimal filter is equal to the number of measurements. Both continuous-time and discrete-time results are presented. An explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix.

This paper is devoted to solving the problem of stabilising an uncertain discrete linear repetitive process, where the model uncertainty is a result of the variable along the pass uncertainty of the parameters. The analysis is applied to the engineering example of the material rolling process, which can be modelled as a repetitive process (Rogers and Owens, 1992; Gałkowski et al., 2003b). Due t...

Deriving the form of the optimal solution of a maximum entropy problem, we obtain an infinite family of linear inequalities characterizing the polytope of spin correlation matrices. For n ≤ 6, the facet description of such a polytope is provided through a minimal system of Bell-type inequalities.

In this paper, some sharp inequalities for certain multilinear operators related to the Littlewood-Paley operator and the Marcinkiewicz operator are obtained. As an application, we obtain the (L p , L q)-norm inequalities and Morrey spaces boundedness for the multilinear operators.

In this paper we solve the open problem, finding the solutions for privacy-preserving horizontally partitioned linear programs with inequality constraints, proposed recently by Mangasarian, O.L. ( Privacy-preserving horizontally partitioned linear programs, Optim Lett 2011, to appear).

We discuss a comparison of the entropy of pseudo-Anosov maps and the volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both directions under some bounded geometry condition. Based on the experiments, we present various observations on the relation between minimal entropies and volumes, and on bounding ...

We study special linear systems called “very special” whose dimension does not satisfy a Clifford type inequality given by Huisman. We classify all these very special linear systems when they are compounded of an involution. Examples of very special linear systems that are simple are also given.